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4 Key Advantages ofUsing Mathematical
Optimization Insteadof Heuristics
Management Paper

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Management Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics

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4 Key Advantages of Using Mathematical
Optimization Instead of Heuristics

When attacking a complex andchallenging business problem,operations research (OR)professionals, software developers,
and data scientists today have manydifferent weapons in their algorithmic
arsenals to choose from.
Broadly speaking, the two mostcommon problem-solving approachesare heuristics and mathematicaloptimization. Although these twoapproaches share the same aim – toprovide a solution to a complicated,
real-world business problem – theirfundamental techniques and their
final results are significantly different.
Two Different Problem-Solving
Approaches

solution to an optimization problem. Many
common metaheuristics, such as genetic
algorithms, simulated annealing, and ant
colony optimization, are actually inspiredby natural phenomena.
In contrast to heuristics, mathematicaloptimization is a declarative, algorithmic
problem-solving approach that is capableof consistently delivering the best possible
solution to business problems.
With mathematical optimization, companies
can capture the key features (decisionvariables, constraints, and businessobjectives) of their business problems in an
optimization model. Using a mathematicalprogramming solver like Gurobi, they cangenerate globally optimal solutions anduse them as the basis to make optimalbusiness decisions.

Heuristics is a popular and practicalproblem-solving approach that employs
techniques designed to provide a fastand feasible (but not necessarily optimal)
solution to a specific problem.
Commonly used in computer science,heuristic algorithms are capable of providing
satisfactory solutions to business problems
in a relatively short timeframe, but in doing
so often sacrifice optimality and accuracy.
Metaheuristics is a widely-used type ofheuristics that came to prominence in the
1990s. It’s designed to identify, develop, or
select a partial search algorithm that may
produce a reasonably good, approximate

Management Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics

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4 Key Advantages of Using Mathematical
Optimization Instead of Heuristics

Expanding Capabilities,
Changing Perceptions
In the past, many companies opted to use
heuristics becuse they were seen as botheasier and faster to implement and able toquickly provide “good-enough” solutions.
Historically, mathematical optimization
technologies were often viewed as toocomplex (requiring specific technicalexpertise) and not able to scale well for
real-world problems.
This perception has changed immensely
over the last few decades with theimprovements in computing power andparallelization. In addition, the introductionof cutting-edge algorithms have mademathematical optimization technologiesmuch more widely accessible andapplicable. Now, we see a rapidly increasing
number of companies across an everexpanding range of industries (including
supply chain, electrical power, finance,aviation, retail, telecommunications, andsports scheduling) applying mathematicaloptimization and achieving significant
business benefits.
Still, many companies continue to develop
and use heuristic solutions – which may
be a part of legacy systems that have beenin place for some time – to address theirbusiness challenges. More and more ofthese companies, however, are finding thatheuristics are not able to meet their needs
and are looking for an alternativealgorithmic approach.

In this Management Paper, we highlight thefour key advantages of using mathematicaloptimization rather than heuristics as aproblem-solving approach.

Key Advantage #1: Mathematicaloptimization gives you the capability
to rapidly and consistently generate
a globally optimal solution.
Mathematical optimization solvers like
Gurobi are able to efficiently process all
available data and consider an astronomical
number of combinations of all relevant
decision variables, constraints, andbusiness objectives. They automatically andswiftly produce the globally optimal solutionthat maximizes your company’s efficiency.
With heuristics, there’s no guarantee thatthe solution will be optimal. In addition, itis very difficult to detect the infeasibility ofoptimization problems with a heuristic.
Mathematical optimization has been used
to tackle many of the world’s toughest
business challenges, like the highly
complicated scheduling problem faced by
the National Football League (NFL).

Management Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics

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4 Key Advantages of Using Mathematical
Optimization Instead of Heuristics

Up until the past decade, the NFL’s planners
utilized heuristic tools and techniques (theyactually hung a wooden, 6-foot squareboard on the wall and used it to map out
who would play whom, when, and where)
and it took them 10 weeks just to figure out
a few feasible schedules for their 17-weekseason. The NFL decided to implement
Gurobi’s mathematical optimization solver
in 2013. Now, they’re able to automaticallycreate and compare over 10,000 feasible
schedules that take into account theirnumerous decision variables andconstraints and find the optimal schedulethat meets all their business objectives.
This is just one example of an organizationthat has made the switch from a heuristicsbased approach to mathematicaloptimization and reaped tremendous
business benefits. A large number ofbusinesses around the globe and acrossvarious industries have decided to utilize
mathematical optimization algorithms
rather than heuristics to address theirbusiness challenges.
When it comes to the quality of the solutiondelivered, heuristics simply cannot comparewith mathematical optimization, which iscapable of generating a globally optimal
solution to any real-world business problem.
Even in business situations where finding
the optimal solution is not required, themathematical optimization technology user
can set a parameter called the optimality
gap that defines how close from the optimal
objective function value a solution can beto stop the optimization process. This is notpossible to do with heuristics.

Key Advantage #2: Mathematicaloptimization applications are easier tomaintain than heuristics.
In today’s volatile and complex businessworld, companies need to have theability to quickly adapt and react toconstantly changing business conditions.
Mathematical optimization gives them thatcapability due to its declarative nature.
As mentioned previously, mathematicaloptimization captures all the key features(decision variables, constraints, or objectivefunctions) of a business problem as an
optimization model. These features are fed
to a solver, like Gurobi, that automaticallychurns out the optimal solution. Whenbusiness conditions change, all you needto do is modify the model and make thenecessary adjustments to these key
features since the underlying mathematicalprogramming engine and algorithms always
remain the same. This flexibility makes
mathematical optimization applications
easier to maintain than their heuristic
counterparts.

Management Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics

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4 Key Advantages of Using Mathematical
Optimization Instead of Heuristics

Indeed, changes in the businessenvironment can wreak havoc on heuristic
algorithms, often making it necessary for
you to make major modifications or evenrewrite the whole heuristic from scratch.
Such algorithmic tuning is not required withmathematical optimization, which is able
to easily incorporate and accommodatechanges to business conditions andcontinuously meet your company’s evolving
business needs.

Key Advantage #3: Mathematicaloptimization can be used inconjunction with heuristics –and can actually strengthen
and improve them.
Deciding whether to use heuristics ormathematical optimization doesn’t haveto be a “one or the other” choice. The
two approaches can be deployed in acomplementary manner.

Provide a systematic solution withbounds on how close that solution
comes to the optimal one.
Through this hybrid solution approach,mathematical optimization solvers canactually strengthen heuristics.
It’s important to note that heuristics
can also be used to help mathematicaloptimization by finding feasible solutions
to determine bounds and enhance thepruning of the solution search tree of themathematical optimization approach.
Many companies – especially those thathave been using heuristics as a part ofa legacy system – do not want to totallyabandon the heuristics approach. By
adopting this hybrid solution approachand running their heuristics through amathematical optimization solver, they cansolve their heuristics (or pieces of them) to
optimality and improve the overall quality of
their solution.

A heuristic algorithm can be fed into amathematical optimization solver, which isable to:Automatically generate an optimalsolution for the heuristic, orDecompose the problem intosubproblems, each of which isformulated as a mathematicaloptimization problem, solved tooptimality, and then combined togenerate the heuristic solution forthe original problem, orManagement Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics

44 Key Advantages of Using Mathematical
Optimization Instead of Heuristics

Key Advantage #4: Mathematicaloptimization enables companies
to achieve the highest levels ofefficiency.
Mathematical optimization automaticallyand rapidly generates the best possible
solution for your real-world combinatorial
problems, then suggests a course ofaction that optimizes the efficiency of yourbusiness processes. But what exactly do
we mean by “optimizing efficiency?” That
depends on your company’s businessobjectives…
In a mathematical optimization model,
you can define exactly what it means
to “optimize efficiency” depending on
your business objectives. Those could
be maximizing profits, minimizing costs,
maximizing on-time performance, orother objectives. Often, companies havenumerous (and sometimes conflicting)business objectives and mathematicaloptimization solvers enable them tooptimally balance the tradeoffs between
these objectives.

The heuristics approach simply cannot
guarantee such a solution.
Mathematical optimization is being usedby leading companies around the world andacross numerous industries to solve theircomplex, real-world business problems,
make optimal business decisions, andreach new heights of efficiency.
For this reason and the reasons highlighted
above, proponents and practitioners of
the heuristics approach would be wise toexplore the capabilities of mathematicalprogramming solvers and experience thepower of mathematical optimization.

No matter what your company’s businessobjectives are or how complex yourbusiness problems are, mathematicaloptimization is able to provide a globally
optimal solution or tell you how close fromthe optimal objective value your current
solution is. In any case, you can use
mathematical optimization to make optimalor near optimal decisions that maximize
your efficiency and overall profitability.

Management Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics5

www.gurobi.com

info@gurobi.com

1 (713) 871-9341

Management Paper: 4 Key Advantages of Using Mathematical Optimization Instead of Heuristics

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